Minimax vs. Consistency

[ ]c n[ ]c n[ ]c n

2

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n

Unconstrained Recovery

Smoothest approximation approach:

3

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n

Unconstrained Recovery

Minimax approach:Feasible set:

Worst case design:

4

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n Unconstrained RecoveryComparison with common

methodsBicubic Bicubic

InterpolationInterpolationMinimaxMinimax

5

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n

Constrained Recovery

Consistent approach:

6

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n

Unconstrained Recovery

Minimax regret approach:Feasible set:

Worst case design:

7

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n

Unconstrained Recovery

Minimax regret approach:Feasible set:

Worst case design:

8

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n Constrained RecoveryTriangular Kernel (Linear

Interpolation)ConsistentConsistent Minimax RegretMinimax Regret

9

[ ]c n[ ]c n[ ]c n[ ]c n[ ]c n

Constrained RecoveryComparison when L=I